Forward and Adjoint Modeling of Sensitivities to Periodic Forcings in Groundwater Flow and Transport

Sensitivity analysis requires the calculation of the sensitivity of a performance measure of model output to a model input. This work focuses on calculating the sensitivity to parameters of a time-periodic forcing that represents either a source or sink. Two methods—the Green’s function method and the adjoint method—are presented for calculating the sensitivity in an efficient manner, by solving for a response function that is independent of the forcing parameters, and performing a convolution of the response function with temporal functions related to the periodic forcing. The Green’s function method calculates the sensitivity of a performance measure at many locations to parameter of a forcing at a single location by solving the forward model. The adjoint method calculates sensitivity of a performance measure at a single location to a parameter of a forcing at many locations by solving the adjoint of the forward model. The results show that both methods produce equivalent results. The adjoint method is more computationally efficient if there are more possible source (or sink) locations than locations at which the sensitivity is desired; while the Green’s function method is more computationally efficient if there are fewer source (or sink) locations than locations at which the sensitivity is desired.